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Differential Topology is the study of the global, shape-related properties of smooth spaces (manifolds) and smooth maps between them, focusing on features that persist under smooth deformations rather than on distances or angles. Books in this category cover foundations such as smooth manifolds, tangent bundles, and smooth maps, and core tools like Sard’s theorem, transversality, degree theory, Morse theory, and handle/cobordism techniques, as well as embedding and immersion theorems. They range from introductory textbooks to advanced monographs on topics like h-cobordism, surgery theory, and the classification of manifolds, with connections to geometry, topology, dynamical systems, and mathematical physics. Intended for advanced undergraduates, graduate students, and researchers, these works typically assume background in calculus, linear algebra, and basic topology.

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